(\partial)/(\partial x)((-x^4+7x^2+3y)^6)

解答

\frac{\partial}{\partial x} ((- x^{4} + 7 x^{2} + 3 y)^{6})

6 (- x^{4} + 7 x^{2} + 3 y)^{5} (- 4 x^{3} + 14 x)

求解步骤

\frac{\partial}{\partial x} ((- x^{4} + 7 x^{2} + 3 y)^{6})

将

y

视为常数

使用连锁律:

6 (- x^{4} + 7 x^{2} + 3 y)^{5} \frac{\partial}{\partial x} (- x^{4} + 7 x^{2} + 3 y)

= 6 (- x^{4} + 7 x^{2} + 3 y)^{5} \frac{\partial}{\partial x} (- x^{4} + 7 x^{2} + 3 y)

\frac{\partial}{\partial x} (- x^{4} + 7 x^{2} + 3 y) = - 4 x^{3} + 14 x

= 6 (- x^{4} + 7 x^{2} + 3 y)^{5} (- 4 x^{3} + 14 x)

(y - x y + x - 1) d x + x^{2} d y = 0

\int \frac{x + 49}{x} d x

\int \frac{x ^{3} ( 1 )}{1 - x ^{8}} d x

\frac{d}{d t} (- e^{- t} sin (t) + e^{- t} cos (t))

d er i v a t i v e \frac{2 x ^{2}}{5}